1. A logistics specialist for Charm City Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are:

Assembly Plant

1 2 3 Supply

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A 6 10 14 200

Factory B 2 2 6 400

C 2 8 7 200

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Demand 220 320 200

The specialist wants to distribute at least 100 cases of parts from factory B to assembly plant 2.

(a) Formulate a linear programming problem to minimize total cost for this transportation problem.

(b) Solve the linear programming formulation from part (a) by using either Excel or QM for Windows. Find and interpret the optimal solution and optimal value. Please also include the computer output with your submission.

The following questions are mathematical modeling questions. Please answer by defining decision variables, objective function, and all the constraints. Write all details of the formulation. Please do NOT solve the problems after formulating.

2. A congressmans district has recently been allocated $45 million for projects. The congressman has decided to allocate the money to four ongoing projects. However, the congressman wants to allocate the money in a way that will gain him the most votes in the upcoming election. The details of the four projects and votes per dollar for each project are given below.

Project Votes/dollar

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Parks 0.07

Education 0.08

Roads 0.09

Health Care 0.11

Family Welfare 0.08

In order to also satisfy some local influential citizens, he must meet the following guidelines.

- None of the projects can receive more than 30% of the total allocation.

- The amount allocated to education cannot exceed the amount allocated to health care.

- The amount allocated to roads must be equal to or more than the amount spent on parks.

- All of the money must be allocated.

Formulate a linear programming model for the above situation by determining

(a) The decision variables

(b) Determine the objective function. What does it represent?

(c) Determine all the constraints. Briefly describe what each constraint represents.

Note: Do NOT solve the problem after formulating.

3. An ad campaign for a trip to Greece will be conducted in a limited geographical area and can use TV time, radio time, newspaper ads, and magazine ads. Information about each medium is shown below.

Medium	Cost Per Ad	Number Reached
TV	8500	12000
Radio	1800	4000
Newspaper	2400	5500
Magazine	2200	4500

The number of TV ads cannot be more than 4. Each of the media must have at least two ads. The total number of Magazine ads and Newspaper ads must be more than the total number of Radio ads and TV ads. There must be at least a total of 12 ads. The advertising budget is $50,000. The objective is to maximize the total number reached.

Formulate a linear programming model for the above situation by determining

(a) The decision variables

(b) Determine the objective function. What does it represent?

(c) Determine all the constraints. Briefly describe what each constraint represents.

Note: Do NOT solve the problem after formulating.

4. The Charm City Vacuum Company wants to assign three salespersons to three sales regions. Given their experiences, the salespersons are able to cover the regions in different amounts of time. The amount of time (days) required by each salesperson to cover each region is shown in the following table:

Region (days)

Salesperson I II III

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A 11 18 12

B 11 15 14

C 10 14 16

However, because of his health reason, salesperson C does not want to be assigned to region II.

The Company wants to assign either salesperson A or salesperson C to region I. The objective is to minimize total time of covering the three sales regions.

(a) The decision variables

(b) Determine the objective function. What does it represent?

(c) Determine all the constraints. Briefly describe what each constraint represents.

Note: Do NOT solve the problem after formulating.